People often associate sweep picking with arpeggios. But it is important to realize that arpeggios are simply chords whose notes are played individually. Sweep picking is simply a technique for playing arpeggios (Jazz trumpet players play arpeggios but you can be sure they are not sweep picking them - maybe sweep blowing?)
The exercises in this lesson go over a particular type of arpeggio called the triad. If you want to learn a little about the theory behind triads, then check out the Diatonic Scale section. I give a brief overview there. Basically, if we were to examine all 7 diatonic scale modes and form triads by taking the 1st, 3rd, and 5th notes of each scale, we would find that there are only 3 unique triads. These are the Major, Minor, and Diminished triads. I have indicated them in 3, 4, and 5 string form and you should become comfortable with them in that order.
Make sure that when you play the exercises you don't let the notes bleed into one another. I recommend that once you get up to speed, you record yourself and then use a program like Cool Edit Pro to slow down the recording and confirm that you are indeed playing all the notes. It is easy to muffle them (i.e. they get lost in the sweeping motion) and evaluating recordings will help you assess where you stand.
This exercise shows you how to play a Major triad arpeggio using sweep picking. It is about as basic as a sweep picking exercise can get, and will serve as the foundation for more difficult exercises. The triad in this example is a C Major. In any key, there are 3 Major triads you could play. They go along with the 1st, 4th, and 5th notes of the Major scale (i.e. the Major, Lydian, and Mixolydian modes). In the key of G, you could play G Major, C Major, or D Major triads.
Here is a familiar Major triad arpeggio shape on the fretboard. This is the most common shape that you will see when it comes to triads. For this exercise, we are just dealing with the E, B and G string.
The Tab shows you what types of pick strokes to use when playing this triad. Start with a down stroke. After the hammer-on and pull-off, you will then descend with an upstroke. Note that the first note is played with a downstroke only the first time it is played. So don't be confused by the downstroke that is shown at the beginning. That downstroke is replaced with an upstroke for the remainder of the exercises (i.e. for as long as you repeat it).